Problem: $ B = \left[\begin{array}{rr}1 & 1 \\ 0 & 1 \\ -2 & -2\end{array}\right]$ $ C = \left[\begin{array}{rr}-2 & 4 \\ 3 & 4 \\ 3 & 2\end{array}\right]$ Is $ B- C$ defined?
Solution: In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ B$ is of dimension $( m \times  n)$ and $ C$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ B$ ) must equal $ p$ (number of rows in $ C$ ) and 2. $ n$ (number of columns in $ B$ ) must equal $ q$ (number of columns in $ C$ Do $ B$ and $ C$ have the same number of rows? Yes Yes No Yes Do $ B$ and $ C$ have the same number of columns? Yes Yes No Yes Since $ B$ has the same dimensions $(3\times2)$ as $ C$ $(3\times2)$, $ B- C$ is defined.